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 Mat. Zametki, 2015, Volume 97, Issue 4, Pages 516–528 (Mi mz10645)

Injectors in Fitting Sets of Finite Groups

N. T. Vorob'ev, M. G. Semenov

Vitebsk State University named after P. M. Masherov

Abstract: A set of subgroups $\mathscr F$ of a finite group $G$ is referred to as a Fitting set if it is closed with respect to taking normal subgroups, products of normal $\mathscr F$-subgroups, and inner automorphisms of $G$. A Fitting set $\mathscr F$ of a group $G$ is said to be $\pi$-saturated if $H\in\mathscr F$ for every subgroup $H$ in $G$ such that $O^{\pi'}(H)\in\mathscr F$. In the paper, it is proved that, if $\mathscr F$ is a $\pi$-saturated Fitting set of a $\pi$-solvable group $G$, then there are $\mathscr F$-injectors in $G$ and every two of them are conjugate.

Keywords: finite group, Fitting set, $\pi$-solvable group, $\pi$-saturated Fitting set.

DOI: https://doi.org/10.4213/mzm10645

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English version:
Mathematical Notes, 2015, 97:4, 521–530

Bibliographic databases:

Document Type: Article
UDC: 512.542
Revised: 23.04.2014

Citation: N. T. Vorob'ev, M. G. Semenov, “Injectors in Fitting Sets of Finite Groups”, Mat. Zametki, 97:4 (2015), 516–528; Math. Notes, 97:4 (2015), 521–530

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10645
• https://doi.org/10.4213/mzm10645
• http://mi.mathnet.ru/eng/mz/v97/i4/p516

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This publication is cited in the following articles:
1. Yang N., Guo W., Vorob'ev N.T., “On F-Injectors of Fitting Set of a Finite Group”, Commun. Algebr., 46:1 (2018), 217–229
2. Yang N., Vorob'ev N.T., Vasilevich T.B., “on Injectors of a Hartley Set of a Finite Group”, Algebr. Colloq., 25:4 (2018), 671–680
3. N. T. Vorob'ev, T. B. Karaulova, “Hartley Sets and Injectors of a Finite Group”, Math. Notes, 105:2 (2019), 204–215
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